A&A 476, 243–253 (2007) Astronomy DOI: 10.1051/0004-6361:20078445 & c ESO 2007 Astrophysics

Deep near-infrared photometry of the globular cluster . Reconciling theory and observations

M. Salaris1,E.V.Held2, S. Ortolani3, M. Gullieuszik2,andY.Momany2

1 Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Egerton Wharf Birkenhead CH41, 1LD, UK e-mail: [email protected] 2 Osservatorio Astronomico di Padova, INAF, vicolo dell’Osservatorio 5, 35122 Padova, Italy e-mail: [enrico.held;marco.gullieuszik;yazan.almomany]@oapd.inaf.it 3 Dipartimento di Astronomia, Università di Padova, vicolo dell’Osservatorio 3, 35122 Padova, Italy e-mail: [email protected] Received 8 August 2007 / Accepted 3 October 2007

ABSTRACT

Context. The Galactic globular cluster 47 Tucanae is central to studies of formation, and a test-bed for theoretical models, distance determination and extragalactic age-dating techniques. Independent parallax-based distance determinations in the optical spectral range provide discrepant results; also, counts along the Red Giant Branch from optical data have disclosed a worrying disagreement with theoretical predictions, that impacts not only the theory of red giant , but also the calibration of the age scale of extragalactic systems. Aims. Our new near-infrared data for 47 Tuc set constraints on its distance and test the reliability of theoretical red giant branch star counts, independently of previous conclusions from optical work. Methods. We have obtained deep near-infrared imaging of 47 Tuc using SOFI at the ESO New Technology Telescope. Colour−magnitude diagrams, isochrones and synthetic horizontal branch modelling have been used to determine the distance of 47 Tuc and constrain its age. We have also constructed a function of red giant stars, which has been compared with theo- retical predictions of models. Results. We obtain a distance (m − M)0 = 13.18 ± 0.03 (random) ± 0.04 (systematic), for [Fe/H] = −0.7 ± 0.1andE(B − V) = 0.04±0.02. This supports the shorter end of the range of distances obtained from optical studies. The mean horizontal branch star is between 0.65 and 0.66 M, and its 1σ Gaussian dispersion is between 0.010 and 0.012 M. The cluster age can only be approxi- mately estimated from the data, and is between ∼10 and ∼13 Gyr. The luminosity function of red giant branch (and early-asymptotic giant branch) stars does not show a statistically significant discrepancy with theory. The brightness of the red giant branch bump in the near-infrared is possibly fainter than the models, although the uncertainty on the spectroscopic metallicity and age prevents to reach a firm conclusion on this issue. Key words. globular clusters: individual: 47 Tuc – infrared: stars – stars: distances – stars: luminosity function, mass function – stars: population II

1. Introduction therein) employed to calibrate the Galactic and extragalactic dis- tance scale. The metal-rich globular cluster 47 Tucanae (NGC 104) has played and continues to play a fundamental role in both Galactic The integrated properties of 47 Tuc play an important role and extragalactic studies. First of all, 47 Tuc belongs to the for testing methods to estimate the mean age and metallicity “thick disk” population of Galactic globular clusters (GCs), and of extragalactic systems. To derive reliable information about the comparison of its age with that of the more metal-poor stellar age and metallicity from the integrated light of unre- solved one must overcome the age-metallicity degen- “halo” GCs and the oldest “thin disk” open clusters provides ff clues about the timescale for the formation of the Galactic stel- eracy, which a ects both integrated colours and absorption- lar populations (Salaris & Weiss 1998; Liu & Chaboyer 2000; line strengths (Worthey 1994). Age-dating techniques based on VandenBerg 2000; Salaris et al. 2004b). It also provides the zero the Balmer lines (Jones & Worthey 1995) have shown great point for the age determination of “bulge” GCs, since their ages promise in breaking this degeneracy, but they need to be tested are most reliably determined from the differential comparison of on Galactic GCs for which independent age estimates based their colour−magnitude diagrams (CMDs) with that of 47 Tuc on their resolved stellar populations are possible. Gibson et al. (Ortolani et al. 1995). Moreover, 47 Tuc has been used as test- (1999) applied the Hγ-Fe4668 line indices diagram to the determi- bed to compare different distance determination methods (such nation of the age of 47 Tuc from its integrated spectrum, obtain- ing an age well in excess of 20 Gyr, much larger than CMD ages, as white dwarf-fitting, main sequence-fitting, red clump method; − see, e.g., Zoccali et al. 2001; Percival et al. 2002, and references currently estimated in the range 11 13 Gyr. Vazdekis et al. (2001) and Schiavon et al. (2002) have in-  Based on data collected at the European Southern Observatory, vestigated this issue in detail. In their analysis of the prob- La Silla, Chile, Proposal 66.B–0247. lem, Schiavon et al. (2002) compared the observed differential

Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20078445 244 M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations luminosity function (star counts as a function of magnitude – LF) Table 1. The journal of observations of 47 Tuc. of the cluster’s stars, with theoretical counterparts from differ- ent authors; this comparison disclosed a worrying discrepancy Field RA(J2000) Dec(J2000) Filter Nima DIT × NDIT (s) along the upper red giant branch (RGB) that, according to the deep 00:24:09.5 −72:02:59 J 310× 6 authors, could be one of the main causes of the spectroscopic- H 35× 12 × CMD age problem. The predicted number of RGB stars above Ks 3512 the horizontal branch appears to be about a factor of 2 lower than shallow 00:24:08.7 −72:03:53 J 31.18× 10 × observed. This discrepancy found by Schiavon et al. (2002) adds H 31.1810 K 31.18× 10 to the discrepancy between predicted and observed values of the s quantity Rbump (ratio between star counts across the RGB bump and fainter RGB stars) introduced by Bono et al. (2001). The  σ exposures were obtained about 2 off the cluster centre to observed value of Rbump for 47 Tuc is more than 2 larger than ff the theoretical predictions, whereas for almost all other clusters avoid the most crowded regions, while the o set was somewhat in the sample of Bono et al. (2001) no significant disagreement smaller for the shallow exposures. A typical observing sequence in each filter consists of 3 images of 47 Tuc interspersed with is found. Given that the luminosity function of RGB stars tests ff the composition stratification above the outward moving thin 3 frames on o set sky positions. The center of our 47 Tuc point- H-shell (Renzini & Fusi Pecci 1988; Cassisi et al. 2002), dif- ings is given in Table 1, together with the number of images in ferences between predicted and observed RGB luminosity func- each filter (3 dithered images were obtained in each of the JHKs / filters), and on-target total exposure times given as the product of tions may be caused by additional physics (e.g. rotation and or × additional element transport mechanisms) not included in the DIT NDIT (the number of integrations co-added before read- model computations. out). In this paper we present the deepest to date near-infrared Observations of 4 standard stars from Persson et al. (1998) were obtained on the same night as the 47 Tuc data for calibra- (near-IR) CMD of 47 Tuc, in the 2MASS JHKs system; its well populated RGB allows us to reassess the extent of the dis- tion purposes. agreement between observed and predicted star counts along the cluster RGB. Apart from minimising the effect of extinc- 2.2. Pre-reduction tion, the advantage of using near-IR filters is that they bracket the spectral region of maximum flux density for RGB stars, plus Our pre-reduction, photometry, and calibration procedures are the bolometric corrections are essentially unaffected by the star similar to those used by Momany et al. (2003) in a deep near- chemical composition. We also provide a new estimate of the infrared study of the globular cluster NGC 6528, using a sim- cluster distance and mean mass loss along the RGB, by fitting ilar data set and the same observing strategy. We only briefly synthetic horizontal branch (HB) models to the observed coun- comment here on the reduction process, and refer the reader to terpart. Constraints on the cluster age from the Turn Off region that study for details. In short, for each set of 47 Tuc images, of the CMD will also be discussed. The whole theoretical anal- a median background frame was created from the 3 sky frames ysis has been performed employing the recent and widely used scaled to a common level, and subtracted from the individual BaSTI library of stellar models and isochrones by Pietrinferni science images. The background-subtracted images were flat- et al. (2004, 2006). fielded and cleaned using master flat-fields, filter-dependent il- The paper is structured as follows. Section 2 describes the lumination corrections, and bad pixel masks available from the observations and data reduction procedures, while the observed ESO SOFI webpages. CMD and luminosity function are presented in Sect. 3. Section 4 compares the CMD with theoretical isochrones and presents a 2.3. Stellar photometry determination of the cluster distance and age. The comparison of observed and predicted star counts is performed in Sect. 5, Point-spread-function (PSF) fitting stellar photometry was indi- followed in Sect. 6 by a summary of the results and conclusions. vidually carried out on the shallow and deep images using the daophot II and allframe (e.g., Stetson 1994). We derived an independent PSF for each image by picking a number of bright 2. Observations and data reduction and isolated stars; the final PSFs were generated with a “Penny” function and quadratic dependence on the position on the frame. 2.1. Observations Following the standard allframe procedure, the 9 deep and Near infrared JHKs observations of 47 Tuc were carried out 9 shallow images were aligned and combined to obtain a me- on Nov. 12, 2000 under stable photometric conditions and see- dian image, upon which a master list was generated, containing ing <0.9 arcsec. We used the SOFI infrared camera mounted at accurate positions of bright and faint stars on the same coordi- the ESO/NTT, equipped with a Hawaii HgCdTe 1024×1024 pix- nate system. Using allframe with that master list, we finally els array detector. The large field mode with 0. 29 pixel was obtained 2 catalogues (separately for the deep and shallow pho-   used for all observations, yielding a 4.9 × 4.9 field-of-view. tometry) by matching the J, H,andKs photometry files. The readout mode was Double Correlated Read, with a readout . . −/ noise 2 1 ADU and gain 5 53 e ADU. 2.4. Calibration Table 1 reports the journal of observations of 47 Tuc. We ob- tained deep and shallow imaging to increase the dynamic range Our near-IR calibration techniques are described in some detail of our observations, in order to measure bright red giant branch by Gullieuszik et al. (2007), and will be only briefly reviewed (RGB) stars as well as faint stars below the main sequence (MS) here. For each standard star, aperture photometry with increas- turnoff (TO). However, despite using for the shallow images ing aperture radii was used to construct growth curves out to a the shortest detector integration time (DIT) permitted by the 5. 2 radius. The aperture magnitudes of standard stars were nor- instrument, the brightest RGB stars were saturated. The deep malised to 1s exposure time and zero airmass to derive the zero M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations 245

Fig. 1. A comparison between our JHKs magnitudes and the 2MASS photometry of 47 Tuc. Filled circles (in red in the electronic edition) highlight the 3σ clipped stars. The median colour differences are given in each panel along with the standard deviation of the residuals. Note Fig. 2. The photometric errors derived from artificial star experiments the absence of measurable colour terms. on the shallow images, plotted as a function of the magnitude of the retrieved stars. Small dots are the differences between the measured and input magnitudes of artificial stars. The filled squares with the error points and colour terms of the calibration equations (given in bars represent the mean and standard deviation of the error distribution Gullieuszik et al. 2007). The calibration equations thus obtained in 0.5 mag bins. were applied to calibrate the shallow catalogue, after correction of the magnitude scale using aperture photometry of a subset of clean, isolated stars on the best science image in each band. The deep photometry was calibrated by adjusting the instrumental magnitudes onto the zero point of the shallow photometry, using stars in common between the two catalogues. As a check of our independent photometric calibration, we compare in Fig. 1 our shallow photometry of 47 Tuc with the 2MASS magnitudes for stars in common (Skrutskie et al. 2006). Figure 1 shows that our photometry on the LCO system of Persson et al. (1998) is, for all practical purposes, coincident with the 2MASS system. In fact, no meaningful shifts nor resid- ual colour terms are noticed between the two systems.

2.5. Photometric errors and incompleteness In order to quantify the errors and incompleteness affecting the K-band luminosity function of red giant stars, we performed ar- tificial star experiments on our shallow photometry of 47 Tuc. Artificial stars were added to all individual images in the shal- low data set in 10 test runs. In each image 470 stars were added, spatially distributed on a grid such that the minimum distance between two artificial stars is ∼50 pixels, which is much larger Fig. 3. The completeness of our shallow data as measured from the ar- than the PSF diameter (∼14 pixels). This procedure maximizes tificial star experiments. Note the incompleteness in the photometry of the number of simulated stars without increasing the crowding of bright stars close to saturation. the frames. The input colours and magnitudes of the simulated stars were generated following the RGB ridge line of 47 Tuc be- tween Ks = 15 and Ks = 8. The frames including the artifi- cial stars were then reduced, analysed, and calibrated following range 9.5 < Ks < 13. The completeness drops smoothly the same procedures as for the science frames, and the resulting at Ks ∼ 13, reflecting the loss of faint stars. The completeness photometry compared with the input catalogue. The difference of our photometry is also limited on the bright side by saturation between the the input and output magnitudes is shown in Fig. 2. (Ks ∼ 9.5). The number of input artificial stars in each mag- The completeness levels, estimated by comparing the number of nitude bin is at least 200, which implies for the less complete retrieved stars to the total number of simulated stars, are shown (faintest) bins a 0.05 formal Poisson uncertainty on the measured in Fig. 3. Our photometry is clearly complete in the magnitude completeness. 246 M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations

Fig. 6. Observed RGB Ks differential luminosity function (0.2 mag bin Fig. 4. Ks − (J − Ks) CMD of 47 Tuc. Stars brighter than Ks = 14 are taken from the shallow photometry (red in the electronic edition) while size). Error bars display the Poisson error on the star counts in each indi- fainter stars are taken from the deep catalogue. vidual bin. The location of the AGB clump, the HB and the RGB bump is marked.

histograms along the MS only show a broad peak in their dis- tribution. Due to the impossibility of defining the exact TO lo- cation with high precision, we prefer to use the thickness of the subgiant branch (SGB) to constrain the age from comparisons with theoretical isochrones.

3.2. The luminosity function

Figure 6 displays the Ks differential luminosity function (LF – star counts, as a function of the Ks magnitude) of all RGB stars and He-burning stars obtained from our photometry. Two local peaks in the star counts are clearly visible. The fainter peak is the more pronounced, and is mainly due to HB stars; the brighter peak is the asymptotic giant branch (AGB) clump, located at Ks ∼ 10.5, and visible also in the CMDs of Figs. 4 and 5. The displayed LF does not show the presence of the RGB bump, which is in fact located at a brightness that overlaps with the HB. To determine its exact position, we have selected − − Fig. 5. Same as Fig. 4, but for the H (J Ks)CMD. the RGB stars populating our CMD as shown in Fig. 7. The RGB sequence is well delineated and allows for a clear separa- tion from HB and AGB objects. Both differential and cumulative 3. Results (number of stars brighter than Ks, as a function of Ks)LFofthe RGB stars have been computed (Fig. 8). A peak in the differen- 3.1. Colour–magnitude diagrams tial LF and a slope change in the cumulative LF (Fusi Pecci et al. The CMDs of 47 Tuc obtained from our catalogues are shown 1990) mark the position of the bump. Our final determination of in Figs. 4 and 5. These are the deepest near-infrared CMDs the magnitude of the RGB bump in 47 Tuc in shown in Fig. 8. published so far for 47 Tuc, reaching ∼2 mag below the main- The RGB bump location was estimated by measuring the me- sequence turnoff in the Ks band. Saturation prevented photom- dian of the unbinned data around the RGB-bump peak. We find bump bump etry of the brightest RGB stars near the RGB tip; however Ks = 12.047 and J = 12.71. An internal measurement these have been discussed in the literature (see, e.g., Valenti error ∼0.02 mag was obtained by varying the magnitude interval used for computing the median (this is more conservative than, et al. 2004a). For both diagrams, we have plotted stars having   < . e.g., using the formal error of a Gaussian fit to the peak). The to- sharpKs 0 05. The width of the RGB is consistent with the photometric er- tal uncertainty on the RGB bump location, including a 0.02 mag rors shown in Fig. 2. The MS is also quite broad, due to the error on the photometric zero points, is 0.03 mag. Cho & Lee bump increasingly large photometric error of the deep catalogue near (2002) determined from 2MASS data Ks = 12.10 ± 0.10, in Ks ∼ 17. When attempting to determine a fiducial line to use for agreement within the errors with our estimate. The same value the determination of the turnoff position, we found that colour (but with an error bar of ±0.05 mag) is obtained from the results M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations 247

parameter η = 0.4 (although the choice of η is not relevant for the results of our analysis) plus HB models for [Fe/H] = −0.7, a value that agrees with spectroscopic estimates of 47 Tuc iron (Zinn & West 1984; Carretta & Gratton 1997; Kraft & Ivans 2003; Carretta et al. 2004). An iron content [Fe/H] = −0.7 cor- responds to the isochrones with Z = 0.008 and Y = 0.256 in the BASTI database1. The adopted initial He abundance is in line with the estimates of Salaris et al. (2004a) based on the R- parameter. We employed the BaSTI isochrones in the L − Teff plane, transformed to the 2MASS system using the bolometric correc- tions by Bonatto et al. (2004) based on the methods discussed by Girardi et al. (2000).

4.1. Distance determination We have determined the distance to 47 Tuc from the adopted theoretical models using the HB part of our near-IR CMDs. HB stars are traditionally used to determine globular cluster distances from theoretical models/isochrones, given that their ff Fig. 7. Ks − (J − Ks) CMD of 47 Tuc showing the RGB star selection brightness is una ected by the exact value of the cluster age; (darker points). moreover, in our case, the lower MS (that can also be used as distance indicator) is affected by excessively large photometric errors and cannot help constrain the distance. It is interesting to notice from Figs. 4 and 5 that the HB is not really horizontal in these photometric filters, not even for red HB morphologies, due to the trend of the near-IR bolometric corrections with Teff. This means that the HB mass distribution affects not only the colour, but also the brightness of this part of the CMD, even for red morphologies. The cluster distance has been determined by producing syn- thetic HBs (following the technique pioneered by Rood 1973) and comparing separately the number distribution of objects with the J, H and Ks magnitudes to the observed counterpart, us- ing Kolmogorov-Smirnov(KS) tests. We did not use the HB por- tion of our adopted η = 0.4 isochrones, because they would not produce extended HBs (no mass dispersion along the HB) and probably would not match the mean mass evolving along the HB of this specific cluster. More in detail, we first selected as genuine HB stars, all ob- served objects with 10.90 < Ks < 12.25 and (J − Ks) < 0.62 (amounting to about 500 HB stars) and then produced a number of synthetic counterparts, as follows. After setting the total num- Fig. 8. Measurement of the Ks magnitude of the RGB bump in 47 Tuc. ber of objects in the synthetic HB simulation to 1000 (the differ- ff Lower panel:di erential luminosity function of RGB stars. The hatched ence with the total number of observed HB stars is not important region outlines the magnitude interval used to measure the bump level. as long as we use a KS test to compare the two number dis- A vertical line marks the median magnitude of stars in the bump. Upper panel: cumulative LF of RGB stars. Note the clear jump and change in tributions as a function of the brightness), we started randomly the LF slope across the bump location. selecting a value of the MHB from a Gaussian distri- bution centred around a value M, with 1σ dispersion σ(M). Both M and σ(M) are free parameters to be fixed at the of Ferraro et al. (2000), transferred to the 2MASS system using start of the simulation; it is well known (see, e.g., Rood 1973) Valenti et al. (2004b). that M determines the mean colour of the HB and σ(M) the colour extension around this mean value. In case of the JHKs filters, as already remarked, the HB is not really hori- 4. Comparison with theoretical isochrones zontal, hence M and σ(M)alsoaffect the brightness range covered by the HB stars, especially in the Ks filter. After MHB is To compare theory with the observed cluster CMDs we made use determined, a value for the time t since the object arrived on the of the extensive BaSTI database of stellar models and isochrones HB has to be chosen. We determined t by employing a flat proba- (computed for both scaled solar and α-enhanced heavy element bility distribution from zero until tHB,wheretHB is the time spent mixtures) described in Pietrinferni et al. (2004, 2006). α More specifically, we used the -enhanced isochrones 1 We employ the most recent α-enhanced models in the BaSTI ([α/Fe] = 0.4, as in Salaris & Weiss 1998, and in ac- database, recomputed with the low-temperature opacities by Ferguson cordance with the value [α/Fe] ∼ 0.3 measured by Carretta et al. (2005). More details can be found at et al. 2004) computed with the Reimers (1975) mass loss http://www.te.astro.it/BASTI/readme.php 248 M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations in the HB phase, which is practically constant for the MHB range typical of clusters with red HBs. The underlying assumption is that stars are being fed onto the HB at a constant rate. Once MHB and t are fixed, we interpolated among the BaSTI grid of HB models with the same chemical composition as our reference isochrones ([Fe/H] = −0.7, [α/Fe] = 0.4), to deter- mine the absolute JHKs magnitudes of the synthetic HB object; the HB models were computed from an He-core mass and sur- face He abundance derived from a progenitor that reaches the RGB tip at an age of 12−13 Gyr (the exact value of the progen- itor age is, however, not relevant, as long as it is above a few Gyr). These magnitudes are then perturbed by adding a distance modulus (m − M)0 (the third free parameter to be fixed at the start of the simulation) and a Gaussian random error with 1σ dispersion, consistent with the values obtained from the artifi- cial star experiments (typical errors of the order of 0.01 mag or less, in all filters). We used E(B − V) = 0.04 and the extinction law by Rieke & Lebofsky (1985) to transform (m − M)0 into the appropriate apparent distance modulus in J, H and Ks.Dueto the low reddening of 47 Tuc, the extinction in the near-infrared filters is extremely small, between 0.01 and 0.03 mag. Finally, Fig. 9. Region in the M−(m − M)0 parameter space where the KS test the synthetic objects are accepted or rejected by simulating the provides P < 95% in all three photometric bands (see text for details). trend of completeness fractions with the relevant filter. The level of completeness in the HB magnitude range is, however, prac- tically always about 100% (see Fig. 3) so that this correction is essentially negligible. The procedure is repeated until the HB is populated by 1000 objects. The resulting object number distributions with the J, H and Ks magnitudes are then separately compared to the observed counterpart by means of a KS test, for each choice of M, σ(M)and(m − M)0. We accept all combinations of M, σ(M)and(m − M)0 values giving a probability P < 95% that observed and theoretical number distributions are different. We find a consistent set of solutions that satisfies the condition on P simultaneously for all three photometric bands. We ex- plored with the KS test the following (m − M)0, M and σ(M) ranges: 13.10 ≤ (m − M)0 ≤ 13.30, 0.61 ≤M/M ≤ 0.68, 0.0 ≤ σ(M)/M ≤ 0.03. These have been selected on the basis of preliminary simulations, showing how combinations of pa- rameters outside these boundaries produce magnitude distribu- tions macroscopically different from the observed ones. As an example, just a simple comparison of the location of the theo- retical zero age horizontal branch (ZAHB, corresponding to the lower envelope of the observed HB distribution) with the ob- Fig. 10. Observed HB differential luminosity function (filled circles) served CMDs displays a total disagreement for (m−M)0 < 13.10 compared to the α-enhanced synthetic counterpart (continuous line) / = −   = . σ   = . or (m − M)0 > 13.30. with [Fe H] 0.7, M 0 655 M,and ( M ) 0 012 M,as- E B − V = . m − M = . Figure 9 displays the region in the (m − M)0 −M plane suming ( ) 0 04 and ( )0 13 18. where P < 95% for all three photometric filters. The minimum values of P are of the order of 50−55%. The resulting distance modulus is (m − M)0 = 13.18 ± 0.03, − function, and the theoretical counterpart obtained from a simula- where 13.18 is the central value of the (m M) range allowed   = . σ   = . − = < tion with M 0 655 M, ( M ) 0 012 M and (m M)0 by the condition P 95%. Considering HB models from the . BaSTI database with different [Fe/H], we estimate an additional 13 18, a combination of parameters that satisfies the condition systematic error of ±0.04 mag, due to a typical uncertainty of on P. The mean magnitudes of the HB stars in the three photo- ±0.1 dex on 47 Tuc [Fe/H] estimates. The ±0.02 mag uncertainty metric filters are reproduced within 0.01 mag. on E(B − V) gives a negligible contribution to the systematic ff error when added in quadrature to the e ect of metallicity. To 4.2. CMD and theoretical isochrones summarize, we obtain from the theoretical models (m − M)0 = 13.18 ± 0.03(random) ± 0.04(systematic). The mean HB mass Adopting the distance derived above, Figs. 11 and 12 compare M is in the range between 0.65 and 0.66 M, and the dispersion the observed K –(J − Ks)andH –(J − Ks) CMDs with BaSTI σ(M) is between 0.010 and 0.012 M. [Fe/H] = −0.7, [α/Fe] = 0.4 theoretical isochrones for ages of 10 Figure 10 displays, as a visual example (we recall that and 13 Gyr. The isochrones are computed with a mass loss effi- the KS test does not require the data to be binned) a ciency parameter η = 0.4, but this does not affect the location of comparison between the observed HB differential luminosity the RGB. M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations 249

− Fig. 11. Ks –(J Ks) CMD of 47 Tuc compared to 10 and 13 Gyr old, Fig. 12. As in Fig. 11, but for the H –(J − Ks)CMD. [Fe/H] = −0.7 α-enhanced isochrones from the BaSTI database (in red in the electronic edition). A distance modulus (m − M)0 = 13.18 and − = . reddening E(B V) 0 04 have been applied to the models (see text properly normalised, they agree with observations at luminosi- for details). ties below the HB level, whereas they predict about a factor of 2 fewer stars at above the HB. This means that, according to S02, the theoretical slope of the RGB differen- The isochrones follow nicely the sequences described by the tial luminosity function is inconsistent with the one observed in observed CMDs, although one has to take into account that the 47 Tuc. As discussed in detail by S02, this discrepancy affects broad MS does not put strong constraints on the accuracy of spectroscopic ages obtained from Hβ and Hγ absorption feature MS theoretical colours. Some mismatch (models too red) ap- indices, because RGB stars contribute a significant fraction of pears at the base of the RGB but, starting more than a magni- the continuum flux of old stellar populations, even in the blue tude below the bump region, the models reproduce nicely the wavelength range of the age-sensitive absorption features. observed RGB sequence. As discussed before, we cannot deter- Using our new near-IR data we investigate here this very im- mine with any degree of accuracy the position of the TO in the portant issue, and test whether our adopted isochrones are able CMD, therefore we use the vertical thickness of the SGB to put to reproduce the observed number of RGB stars both below and some – admittedly weak – constraints on the cluster age. One can above the HB level. We show here the results obtained from see more clearly from the H –(J − K ) CMD that the SGB of the s RGB star counts in the K band. We checked that the same results 13 Gyr isochrone runs approximately along the faint end of the s are obtained when considering star counts in the J and H pho- observed SGB, whereas the 10 Gyr isochrone is near the upper tometric filters. An important advantage of using near-infrared envelope of the observed SGB. A realistic estimate of the cluster filters is that the bolometric corrections are largely indepen- age is therefore most probably contained between these two lim- dent of metallicity and the metal mixture (Cassisi et al. 2004). its, and this is consistent with independent recent determinations Therefore, the fact that we are using colour transformations to of 12.5±0.5 Gyr (Liu & Chaboyer 2000), 10.9±1.4 Gyr (Salaris the 2MASS system based on scaled solar model atmospheres, et al. 2004b) and 11.5 ± 0.8 Gyr (VandenBerg 2000). whereas the underlying theoretical isochrones are α-enhanced, It is important to notice that the initial MS mass of the stars at does not affect our analysis at all. the RGB tip, for ages between 10 and 13 Gyr, is in the range be- The RGB star selection from the observed Ks −(J−Ks)CMD tween ∼0.95 and ∼0.89 M. A mean mass of ∼0.65 M for the is the same as discussed in Sect. 3. The differential luminos- objects still evolving along the HB means that their RGB pro- ity function (LF) for the RGB stars in the shallow catalogue of genitors have lost 0.24−0.30 M during their RGB ascent. This 47 Tuc – with a bin size of 0.2 mag, with and without corrections amount of mass loss corresponds to η ∼ 0.5intheReimers for the completeness – together with the completeness fraction formula. along the RGB, is displayed in Fig. 13. Since the completeness is always above 90% for Ks between ∼9.5 and ∼14 mag, we will 5. The number of stars along the RGB concentrate our analysis in this region. A preliminary compar- ison of the observed LF with theory is performed in Fig. 14. Schiavon et al. (2002, hereafter S02) discovered a worrying dis- There is an important point to consider when comparing S02 crepancy between the number of RGB stars above the level of and our analysis. In S02, the comparison of the observed LF the HB and the theoretical predictions from independent theo- with theory was performed by normalising the theoretical LF to retical isochrones by both Girardi et al. (2000) and Salaris & the observed one at the TO region. Instead, we have chosen to Weiss (1998). Actually S02 employed α-enhanced isochrones normalise the theoretical LF to the total number of stars (cor- computed with the same code and input physics as in Salaris rected for the small effect of completeness) in the magnitude & Weiss (1998), but including atomic diffusion. Diffusion does range 12.4 < Ks < 13.2. Given that S02 found a discrepancy be- not however alter the shape of the RGB differential luminos- tween theory and observations only along the bright part of the ity function. After theoretical star counts along the RGB are RGB (approximately above the bump+HB region) we should, in 250 M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations

Fig. 13. The logarithm of the observed RGB differential luminosity ff Fig. 14. Logarithm of the observed RGB luminosity function (filled cir- function in Ks. The shaded area highlights the e ect of neglecting the cles – completeness corrections applied) with a 0.2 mag bin-size, com- correction for the completeness. The lower panel shows the value of the pared to the theoretical counterpart for [Fe/H] = −0.7, an age of 11 Gyr completeness fraction as a function of Ks. and (m − M)0 = 13.18. The theoretical LF has been normalised to the observed number of stars in the range 12.4 < Ks < 13.2. Error bars due to Poisson statistics are also displayed. principle, be able to find the same discrepancy, even with our normalisation to the number of RGB stars along a section of the faint RGB sequence. Also, the number of stars populating our consistent with the values obtained from the artificial star ex- LF should be approximately the same as for S02 LF. As a refer- periments (typical errors of the order of 0.01 mag or less, in all ence, S02 give a number of 62 AGB+RGB objects in their LF, in filters). Finally, the synthetic objects are accepted or rejected by the range 12.8 < V < 13.2. Taking advantage of the 47 Tuc mean simulating the trend of completeness fractions with Ks. The total K − (V − K) relations by Ferraro et al. (2000) – again transferred number of stars drawn in the simulation is very large, of the order to the 2MASS system using Valenti et al. (2004b) – and their of 105 objects, to avoid statistical fluctuations in the theoretical adopted distance moduli and reddenings, we have been able to star counts. The difference with the total number of observed estimate the number of objects in the Ks magnitude range cor- RGB stars is not important as long as we use a KS test to com- responding to the V interval given by S02. We find 69 objects, pare unbinned predicted and observed number distributions as a approximately the same as the counterpart in the S02 luminosity function of Ks. We accept the existence of a statistically signif- function. icant difference between theory and observations whenever we Figure 14 shows, at a glance, a general agreement between obtain a probability P > 95% that observed and theoretical num- theory and observations, without a significant offset above the ber distributions are different. RGB bump region, contrary to the results by S02. It is interesting Our reference MC simulation employed [Fe/H] = −0.7, an to notice that the RGB bump is clearly fainter than the models. age of 11.0 Gyr and (m − M)0 = 13.18. If we compare the We will come back to this point later in this section. LFs for the whole RGB with Ks < 14.0, we obtain P ∼ 100%, To avoid binning the data, and to include easily in a more i.e., a very significant discrepancy between theory and observa- quantitative comparison the effect of the – albeit small – pho- tions. Given the general agreement displayed by Fig. 14, we sus- tometric errors and completeness fraction, we again made use pected that this value of P could be mainly due to the discrepant of Monte Carlo (MC) simulations and KS tests in the analy- luminosity of the bump, and we repeated our KS-test analysis sis that follows. Our main aim is to test whether the star num- by dividing the RGB into three magnitude ranges. In the range ber distribution predicted by the theoretical isochrones along 9.5 ≤ Ks ≤ 11.5, above the observed RGB bump, P is always the whole observed RGB sequence is consistent with the ob- smaller than ∼80%. Below the observed bump, for Ks > 12.6, P served counterpart. To this purpose – and in the same vein as is always smaller than 30%. The bump region, 11.5 ≤ Ks ≤ 12.6 the HB distance estimate discussed before – we have produced shows P ∼ 100%. synthetic samples of RGB stars with a MC technique applied To show this discrepancy even more clearly, Fig. 15 com- to the theoretical isochrones. A theoretical isochrone of a given pares the observed and theoretical LF around the bump region, metallicity and age is selected, and the effect of extinction and with a 0.04 mag bin-size. The theoretical LF is normalised as distance modulus is added to the absolute K magnitudes. The in Fig. 14. The different luminosity of the bump is evident; the Salpeter (1955) Initial Mass Function (IMF) has then been used difference between the average Ks of the bump in the observed to draw randomly stellar between the lower and upper and theoretical LF amounts to ∆Ks ∼ 0.15 mag, the theoretical mass limits of the RGB population; the precise choice of the bump being brighter. IMF exponent does not affect the results, given the very narrow In a second set of tests we have considered the combined mass range of the objects populating the RGB. The appropri- number distribution of RGB plus early-AGB stars with Ks < ate Ks magnitude is then assigned to each mass, by interpolating 10.9, that is, the total number of stars above the HB (the HB the- among neighbouring points along the isochrone. These Ks mag- oretical star distribution has been already forced to match the nitudes are then perturbed by a Gaussian 1σ photometric error, observed one in our determination of the cluster distance) that M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations 251

Fig. 15. Observed LF for RGB stars in the bump region (dashed line) Fig. 16. Ks –(J − Ks) CMD of 47 Tuc compared to 13 Gyr old, [Fe/H] = compared to the theoretical counterpart (solid line, in red in the elec- −0.6 α-enhanced isochrones from the BASTI database (in red in the / = − − = . tronic edition) for [Fe H] 0.7, an age of 11 Gyr, (m M)0 13 18 electronic edition). A distance modulus (m − M)K = 13.14 and red- and a 0.04 mag bin size. dening E(B − V) = 0.02 have been applied to the models (see text for details). also contains objects belonging to the AGB-clump. We include isochrone with [Fe/H] = −0.7 and [α/Fe] = 0.4displaysa in this analysis the AGB part of the η = 0.4 isochrones, given ff RGB-bump about 0.15 mag brighter than observations. that the AGB region is una ected by the exact value of the evolv- We have performed additional comparisons by varying some ing mass, for the mass range typical of red HBs. A comparison parameters within realistic ranges, and studied the effect on the of theory with observations using the KS test and the methods α/ ∼ bump luminosity. A decrease of [ Fe] from 0.4 to 0.0 (we recall described before provides P 20%. that Carretta et al. 2004 measured [α/Fe] ∼ 0.3) at fixed [Fe/H] Before closing this section, we also investigate the dis- increases the HB brightness by 0.05 mag in the near-infrared crepancy between predicted and observed values of the quan- bands. This causes an increase of the distance modulus by the tity Rbump, i.e., the ratio between star counts across the same amount, but the bump brightness increases by 0.24 mag, RGB bump and fainter RGB stars, discussed by Bono et al. and therefore the discrepancy between theory and observations (2001). More specifically, Rbump has been defined by Bono et al. is exacerbated. An increase of [Fe/H] by 0.1 dex (typical error (2001) in the Johnson V-band as the ratio between the number associated with the spectroscopic determination for this cluster) bump ± . of RGB stars within V 0 4 and the number of RGB stars at fixed [α/Fe] decreases the distance modulus by ∼0.04, because bump + . ≤ ≤ bump + . within V 0 5 V V 1 5. Rbump relies on star counts of a fainter HB, and the bump brightness decreases by 0.12 mag. that do not depend on the bin size nor on the bump luminosity, The net effect is to reduce the size of the discrepancy by half. and it is a diagnostic of the size of the H-profile discontinuity Changing the age from 11 to 15 Gyr decreases the bump bright- left over by the bottom boundary of the convective envelope at ness by 0.10 mag, keeping the distance modulus unchanged. its largest extension. As a conclusion, a combination [Fe/H] = −0.6, [α/Fe] = 0.4 Ks ∼ − We have determined an equivalent parameter Rbump,defined and an age of 13 14 Gyr would eliminate the discrepancy be- as the ratio of the number of stars within Kbump ± 0.4, to the tween the observed and predicted bump brightness. Figure 16 s displays a comparison between the K –(J − K ) CMD of 47 Tuc number of objects within Kbump + 0.65 ≤ K ≤ Kbump + 1.55. s s s s s and a 13 Gyr isochrone with [Fe/H] = −0.6, [α/Fe] = 0.4, Our data provide RKs = 0.71 ± 0.05. The value predicted from bump (m − M)0 = 13.14 and E(B − V) = 0.02. The quality of the fit our reference 11 Gyr old, [Fe/H] = −0.7, α-enhanced isochrone is very similar to the case of the 13 Gyr, [Fe/H] = −0.7 models; Ks = . is Rbump 0 64, i.e. the discrepancy with observations, is well the reduced reddening is still within the commonly quoted error σ Ks below the 2 level, much less significant than found by Bono bars. The value of Rbump obtained from this isochrone is essen- et al. (2001) from an independent photometry in the BV system. tially unchanged compared to the 11 Gyr, [Fe/H] = −0.7 case, and it would therefore still be within less than 2σ from the ob- served RKs . 5.1. Playing with parameters bump An alternative solution to the problem of the observed bump On the basis of the results discussed before, we can exclude a brightness is to keep the age fixed at 11 Gyr, [Fe/H] = −0.7, significant discrepancy between theoretical and observed trends [α/Fe] = 0.4 and the distance modulus as derived in Sect. 4.1, of star number counts versus Ks along the whole RGB sam- but introduce some degree of overshooting (as a free parame- pled by our data. The same results are obtained considering the ter) from the bottom of the convective envelopes into the sur- number counts as a function of J and H magnitudes. The only rounding, formally stable, radiative regions (Alongi et al. 1991). discrepancy between theory and observation is the position of This results in a thicker convective envelope, deeper location the RGB bump. With our derived distance modulus, a 11 Gyr of the H-profile discontinuity left over by convection at its 252 M. Salaris et al.: Deep near-infrared photometry of the globular cluster 47 Tucanae. Reconciling theory and observations

Table 2. Recent parallax-based distance determinations for 47 Tuc.

Reference Method (m − M)0 E(B − V) Reid (1998) MS fitting 13.56 ± 0.15 0.040 Carretta et al. (2000) MS fitting 13.38 ± 0.09 0.055 Zoccali et al. (2001) White dwarf fitting 13.09 ± 0.14 0.055 . +0.06 Percival et al. (2002) MS fitting 13 25−0.07 0.040 Salaris & Girardi (2002) Red clump 13.19 ± 0.07 0.055 maximum extension, and a fainter bump. Based on the numerical recently discussed by Percival et al. (2002) and Zoccali et al. experiments reported in Cassisi et al. (2002), we estimate that (2001). Percival et al. revised previous MS-fitting determinations an overshooting by ∼0.2 Hp beyond the formal Schwarzschild and, using Kaluzny et al. (1998) recalibrated data, concluded that − = . +0.06 boundary of the convective envelope would eliminate the dis- the dereddened modulus is (m M)0 13 25−0.07, shorter than crepancy. Such a moderate amount of overshooting would not most of the previous results (13.38 from Carretta et al. 2000; ff Ks 13.56 from Reid 1998). Zoccali et al. (2001) derived the distance appreciably a ect the predicted value of Rbump compared to the non-overshooting case (Cassisi et al. 2002). to 47 Tuc from the white dwarfs cooling sequence compared to Also, based on the results by Cassisi et al. (1997), one can in- the local field white dwarfs measured with the same instrument. fer that the inclusion of atomic diffusion would only marginally This method is independent of the HB models as well as of the − = . improve the agreement between predicted and observed bump local subdwarfs. They obtained (m M)0 13 09 assuming − = . brightness, but the efficiency of this process in globular cluster E(B V) 0 055, shorter than the distance of Carretta et al., but σ stars is still very uncertain (Gratton et al. 2001; Korn et al. 2006). compatible – within the 1 errors – with that found by Percival ff − The effect of the parameter (age, chemical composition) et al. (2002). Notice also that the slightly di erent E(B V)val- ff changes discussed before on the comparison of the RGB and ues adopted by di erent authors do not substantially modify the AGB star counts – excluding the RGB bump region – is neg- comparison of their results. The theoretical HB-fitting distance ligible. By repeating the KS tests, we find that the values of P we obtain in this work confirms the relatively “short distance” considering only RGB stars above and below the bump, and for 47 Tuc found by Zoccali et al. (2001) and Percival et al. the combined RGB+AGB objects above the HB, are almost un- (2002). changed compared to the reference case of an 11 Gyr isochrone As a byproduct of the synthetic HB fitting, we obtain a mean   with [Fe/H] = −0.7 and [α/Fe] = 0.4. In any case, P is always HB star mass M in the range between 0.65 and 0.66 M,and σ   well below the 95% threshold. the dispersion ( M ) is between 0.010 and 0.012 M. We note that the adopted distance is also constrained by the Constraints on the cluster age have been obtained by fitting observed location of the AGB bump in 47 Tuc. We found that a theoretical isochrones to the observed CMD, employing the dis- change of the distance modulus of the order of 0.10 mag would tance obtained from the synthetic HB models. We obtain an age destroy the agreement of the RGB+AGB LF, because in this case in the range between ∼10 and ∼13 Gyr, in agreement with pre- the AGB bump region – that is well reproduced with our refer- vious independent estimates. ence distance, and is very weakly sensitive to chemical compo- We have also investigated in detail the level of agreement sition and age (Pulone 1992) – would be badly reproduced by between the theoretical and observed LF of the RGB (and the theoretical models. early-AGB) stars, to verify previous claims of a significant dis- crepancy between theory and observations in 47 Tuc. Using again a KS-test-based technique, we did not find a statisti- 6. Summary and conclusions cally significant disagreement between predicted and observed RGB star counts, over a brightness range of about 5 mag. The We have presented the deepest to date near-IR photometry of only problem concerns the brightness of the RGB bump, which 47 Tuc, a cluster central to studies of Galaxy formation, and a appears to be fainter than theoretical expectations (by ∼0.15 mag testbed for theoretical models, distance determination and extra- in Ks) when adopting as reference values (m − M)0 = 13.18, galactic age-dating techniques. [Fe/H] = −0.7, E(B − V) = 0.04 and an age of 11 Gyr. The We have derived the cluster distance by fitting synthetic discrepancy would disappear by allowing for an overshooting HB models to the observed CMD, in the J, H and Ks bands, ∼ . H − = of 0 2 p beyond the bottom of the convective envelope in using a method based on the KS test. Assuming E(B V) the theoretical stellar models. As an alternative, varying [Fe/H], 0.04 ± 0.02, we have obtained a distance modulus (m − M)0 = . ± . ± . y distance modulus and age within the associated errors, the dis- 13 18 0 03(random) 0 04(s stematic). Once the HB star crepancy also vanishes, without the need to include any substan- distribution is matched by synthetic HB models, the observed tial amount of convective overshooting from the Schwarzschild brightness of the AGB bump is also well reproduced by theory. boundary. The uncertainty on the spectroscopic metallicity and − Our derived distance is almost identical to the value (m age prevent us from reaching a firm conclusion on this issue. = . ± . M)0 13 19 0 07 obtained by Salaris & Girardi (2002), Furthermore, the star counts in the bump region (as who applied their population corrections to the HIPPARCOS parametrised by the quantity RKs ) are not significantly dif- Ks magnitude of the solar neighbourhood Red Clump, and bump used 47 Tuc 2MASS data analysed by Grocholski & Sarajedini ferent from theoretical expectations; this confirms the size of (2002). Table 2 summarises the most recent determinations of the H-profile discontinuity left over by the bottom boundary of 47 Tuc distance modulus, obtained from parallax-based meth- the convective envelope at its largest extension, as predicted by ods2. The distance modulus of 47 Tuc from optical data has been theory. 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